Graph each absolute value function. State the domain, range, and y-intercept.

Answer:The domain is  [tex](-\infty,\infty)[/tex] and its range is [tex][3,\infty).[/tex]The y-intercept is (0,3).Step-by-step explanation:Consider the parent function [tex]y=|x|.[/tex] Its domain is [tex]x\in (-\infty,\infty)[/tex] and its range is [tex]y\in [0,\infty).[/tex]The graph of the function [tex]y=|x|+3[/tex] is obtained from the graph of parent function by translation 3 units up (see diagram). This translation doesn't change the  domain and will change the range of the function, thus the domain is  [tex](-\infty,\infty)[/tex] and its range is [tex][3,\infty).[/tex]To find th y-intercept you have to find y at x=0:[tex]y=|0|+3=3.[/tex]Hence, the y-intercept is (0,3).